Question

1/2+√5 + 1/√5+√6 + 1/√6+√7 + 1/√7+√8 rationalize​

Answer 1

Answer:

(1/2+√5)+(1/√5+√6)+(1/√6+√7)+(1/√7+√8).

(1/2+√5).

Rationalising denominator of (2+√5) is (2-√5).

Multiply numerator & denominator by (2-√5).

(1/2+√5)×2-√5/2-√5.

1(2-√5)/(2)²-(√5)². (Because (a+b)×(a-b)=a²-b² where a=2 & b=√5).

2-√5/4-5.

2-√5/-1. (Because +×-=- & largest number is important).

(-2-√5). (Because +÷-=-).

(1/√5+√6).

Rationalising denominator of (√5+√6) is (√5-√6).

Multiply numerator & denominator by (√5-√6).

(1/√5+√6)×√5-√6/√5-√6.

1(√5-√6)/(√5)²-(√6)². (Because (a+b)×(a-b)=a²-b² where a=√5 & b=√6).

√5-√6/5-6.

√5-√6/-1. (Because +×-=- & largest number is important).

(-√5-√6). (Because +÷-=-).

(1/√6+√7).

Rationalising denominator of (√6+√7) is (√6-√7).

Multiply numerator & denominator by (√6-√7).

(1/√6+√7)×√6-√7/√6-√7.

1(√6-√7)/(√6)²-(√7)². (Because (a+b)×(a-b)=a²-b² where a=√6 & b=√7).

√6-√7/6-7.

√6-√7/-1. (Because +×-=- & largest number is important).

(-√6-√7). (Because +÷-=-).

(1/√7+√8).

Rationalising denominator of (√7+√8) is (√7-√8).

Multiply numerator & denominator by (√7-√8).

(1/√7+√8)×√7-√8/√7-√8.

1(√7-√8)/(√7)²-(√8)². (Because (a+b)×(a-b)=a²-b² where a=√7 & b=√8).

√7-√8/7-8.

√7-√8/-1. (Because +×-=- & largest number is important).

(-√7-√8). (Because +÷-=-).

(1/2+√5)+(1/√5+√6)+(1/√6+√7)+(1/√7+√8)

=(-2-√5)+(-√5-√6)+(-√6-√7)+(-√7-√8).

=-2-√5-√5-√6-√6-√7-√7-√8. (Because +×-=-).

=-2+5+6+7+8. (Because -×-=+, √5×√5=5, √6×√6=6, √7×√7=7 & √8×√8=8).

=-2+26.

=24. (Because -×+=- & largest number is important).

I think this is your answer.